A zero-or-one law in aggregated closed queueing networks

A zero-or-one law in aggregated closed queueing networks For a closed queueing network with single-server nodes, we prove that if the total number of requests, the number of servers in one of the nodes, and service rates in all other nodes are made n times as large, then the stationary number of requests in the multiserver node divided by n converges in probability as n → ∞ to a positive constant, determined by parameters of the original network, with geometric convergence rate. Single-server nodes in the constructed network can be interpreted as repair nodes, the multiserver node as a set of workplaces, and requests as elements in a redundancy-with-repair model. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

A zero-or-one law in aggregated closed queueing networks

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Publisher
SP MAIK Nauka/Interperiodica
Copyright
Copyright © 2011 by Pleiades Publishing, Ltd.
Subject
Engineering; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control; Communications Engineering, Networks
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946011010066
Publisher site
See Article on Publisher Site

Abstract

For a closed queueing network with single-server nodes, we prove that if the total number of requests, the number of servers in one of the nodes, and service rates in all other nodes are made n times as large, then the stationary number of requests in the multiserver node divided by n converges in probability as n → ∞ to a positive constant, determined by parameters of the original network, with geometric convergence rate. Single-server nodes in the constructed network can be interpreted as repair nodes, the multiserver node as a set of workplaces, and requests as elements in a redundancy-with-repair model.

Journal

Problems of Information TransmissionSpringer Journals

Published: Apr 19, 2011

References

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